4/2*X+4/5*y=10

Solution for 4/2*X+4/5*y=10 equation:

4/2X+4/5X=10

We move all terms to the left:

4/2X+4/5X-(10)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R



Domain of the equation: 5X!=0

X!=0/5

X!=0

X∈R


We calculate fractions


20X/10X^2+8X/10X^2-10=0

We multiply all the terms by the denominator


20X+8X-10*10X^2=0

We add all the numbers together, and all the variables

28X-10*10X^2=0

Wy multiply elements

-100X^2+28X=0

a = -100; b = 28; c = 0;
Δ = b2-4ac
Δ = 282-4·(-100)·0
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-28}{2*-100}=\frac{-56}{-200}
=7/25
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+28}{2*-100}=\frac{0}{-200}
=0
$